There are coin lockers on each floor. Some of them are refrigerated, so you can rest assured even after purchasing fresh food. You can continue shopping.
Please check the facility website for details such as locker size.
・Coin lockers
https://mitsui-shopping-park.com/lalaport/anjo/service/locker.html
・Refrigerated locker
https://mitsui-shopping-park.com/lalaport/anjo/service/coldlocker.html